Another weighing problem

[marius.stephant]

We have 22 nickels of which 20 are identical and weigh exactly the same and 2 are fake and are of equal weight but we don't know if they are heavier or lighter than the original ones. Using a balance scale, we want to split the nickels into two groups of equal weight with the least number of weighings. Can you find how many weighings are required?

[mycalsuite]

With just one weighing, you can be sure to divide them into two groups of the same weight:

On either side of the balance, arrange eleven coins.

The groups are equal if the scale is balanced.

If not, carefully switch the coins between the two sides until they are balanced; since only two are phony, this guarantees equality.

Therefore, with possible small changes, minimum weighings = 1.